1. **State the problem:** Find the coordinates of point C where line k crosses the x-axis. 2. **Recall:** The x-axis is where $y=0$. To find the x-intercept of line k, set $y=0$ in its equation and solve for $x$. 3. **From previous parts:** Line l: $2x - 3y = 12$ Point B: $(0, -4)$ Line k passes through B and is perpendicular to l. 4. **Find slope of line l:** Rewrite line l in slope-intercept form: $$2x - 3y = 12 \implies -3y = 12 - 2x \implies y = \frac{2}{3}x - 4$$ Slope of l is $m_l = \frac{2}{3}$. 5. **Slope of line k:** Since k is perpendicular to l, its slope is the negative reciprocal: $$m_k = -\frac{1}{m_l} = -\frac{1}{\frac{2}{3}} = -\frac{3}{2}$$ 6. **Equation of line k:** Using point-slope form with point B(0, -4): $$y - (-4) = -\frac{3}{2}(x - 0) \implies y + 4 = -\frac{3}{2}x \implies y = -\frac{3}{2}x - 4$$ 7. **Find x-intercept C:** Set $y=0$: $$0 = -\frac{3}{2}x - 4$$ Add 4 to both sides: $$4 = -\frac{3}{2}x$$ Divide both sides by $-\frac{3}{2}$: $$x = \frac{4}{-\frac{3}{2}} = 4 \times -\frac{2}{3} = -\frac{8}{3}$$ 8. **Coordinates of C:** $$C = \left(-\frac{8}{3}, 0\right)$$ **Final answer:** The coordinates of point C are $\boxed{\left(-\frac{8}{3}, 0\right)}$.